A position of a person or object may be determined using a global positioning system (GPS) receiver, for example. However, to use a GPS receiver, a GPS antenna coupled to the GPS receiver must have a line of sight to GPS satellites. For increased accuracy, the number of GPS satellites having a line of sight to the GPS antenna increases. In other words, position determining using a GPS receiver will not work indoors, for example, or other location where the GPS antenna does not have a line of sight to the sky.
In such GPS “denied” locations, a person or object may be tracked using an inertial measurement unit (IMU). An inertial measurement unit may cooperate with an accelerometer to calculate displacement, for example. More particularly, a determined acceleration may be first integrated over a time period to determine a velocity. The velocity may be integrated over the time period to determine the displacement. In other words, a double integration is performed on the acceleration to arrive at the displacement.
Velocity drift due to accumulation of errors or noise may contribute to inaccuracies in determining the displacement over the time period. Additionally, gyroscope drift and bias in systems that include a gyroscope, for direction, for example, may also contribute to displacement inaccuracies over the time period.
Moreover, performing the double integration of the determined acceleration over the time period, especially if the time period is relatively long or includes a relatively large amount of data samples from the accelerometer, introduces a relatively large error over the time period. For example, performing a double integration of acceleration measurements made while walking 200 meters in a rectangle may lead to an error in displacement of greater than 8 kilometers, for example.
Referring to FIGS. 1a-1d, to illustrate the error in displacement, acceleration data from two accelerometers is measured over sixty seconds and illustrated by overlapping curves 21, 22, in graph 20 (FIG. 1a). Typical noise/bias numbers in an inertial measurement unit (IMU) are used according to:Acceleration A (t)=(sin(t*2π)+0.00)*0.5*g Acceleration B (t)=(sin(t*2π)+0.05)*0.5*g where t is time, and g is the gravitational constant.
A noise bias of 0.05 G is used. A first integration of the acceleration curves 21, 22 from the graph 20 results in velocity curves 24, 25 in graph 23 illustrated in FIG. 1b. A second integration of the accelerations (i.e. an integration of the velocity) results in displacement lines 27, 28, illustrated in the graph 26 in FIG. 1c. Illustratively, the displacements 27, 28 are separated by about 100 meters. This error is translated in to a distance error, which is illustrated by the curve 29 in graph 30 in FIG. 1d. 
One approach to address the problem of a relatively large error resulting from integration over a relatively short time involves mounting the IMU in a shoe of a human user, for example. The human user's steps or movements are characterized or determined, for example by a zero velocity. A measured acceleration is twice integrated over the time period between the determined steps to calculate the displacement over the time period, or the step. By using each step as the time period for integration, error from integration is reduced compared to integrating over an entire movement. In other words, accumulated errors are thus “zeroed out” after each step.
U.S. Pat. No. 6,522,266 to Soehren et al. discloses navigation system for foot travel. More particularly, Soehren et al. discloses a system that includes an inertial processing unit coupled to a motion sensor. The inertial processing unit determines a first position estimate based upon the motion sensor, and more particularly, a step length. The system also includes a motion classifier to determine a step distance estimate, and a Kalman filter that determines corrective feedback signals based upon a first position estimate, the distance estimate, and past and present values of motion signals.